I'm trying to come up with a slogan. My peer quickly pointed out that this is wrong. He doesn't know why, and I can't figure it out either. What I'm trying to say is, "we have been supplying industry since 1990 and will continue to do so."

Grammatically there isn't anything wrong with that. I suppose industry can be a very general word, do you have anything more specific than "industry" to use? But there isn't anything wrong with your slogan if that is what you want.

MsJen&Co make a good point. What is the product you are supplying and to what industry? You could say for example - 'Supplying the car industry since 1990'. Or you could simply say 'Established 1990'....which is often shortened too 'est. 1990'.